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Simplifying -7 + -9(-4 + -2B) * B = 4 Reorder the terms for easier multiplication: -7 + -9B(-4 + -2B) = 4 -7 + (-4 * -9B + -2B * -9B) = 4 -7 + (36B + 18B2) = 4 Solving -7 + 36B + 18B2 = 4 Solving for variable 'B'. Reorder the terms: -7 + -4 + 36B + 18B2 = 4 + -4 Combine like terms: -7 + -4 = -11 -11 + 36B + 18B2 = 4 + -4 Combine like terms: 4 + -4 = 0 -11 + 36B + 18B2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.6111111111 + 2B + B2 = 0 Move the constant term to the right: Add '0.6111111111' to each side of the equation. -0.6111111111 + 2B + 0.6111111111 + B2 = 0 + 0.6111111111 Reorder the terms: -0.6111111111 + 0.6111111111 + 2B + B2 = 0 + 0.6111111111 Combine like terms: -0.6111111111 + 0.6111111111 = 0.0000000000 0.0000000000 + 2B + B2 = 0 + 0.6111111111 2B + B2 = 0 + 0.6111111111 Combine like terms: 0 + 0.6111111111 = 0.6111111111 2B + B2 = 0.6111111111 The B term is 2B. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2B + 1 + B2 = 0.6111111111 + 1 Reorder the terms: 1 + 2B + B2 = 0.6111111111 + 1 Combine like terms: 0.6111111111 + 1 = 1.6111111111 1 + 2B + B2 = 1.6111111111 Factor a perfect square on the left side: (B + 1)(B + 1) = 1.6111111111 Calculate the square root of the right side: 1.269295518 Break this problem into two subproblems by setting (B + 1) equal to 1.269295518 and -1.269295518.Subproblem 1
B + 1 = 1.269295518 Simplifying B + 1 = 1.269295518 Reorder the terms: 1 + B = 1.269295518 Solving 1 + B = 1.269295518 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + B = 1.269295518 + -1 Combine like terms: 1 + -1 = 0 0 + B = 1.269295518 + -1 B = 1.269295518 + -1 Combine like terms: 1.269295518 + -1 = 0.269295518 B = 0.269295518 Simplifying B = 0.269295518Subproblem 2
B + 1 = -1.269295518 Simplifying B + 1 = -1.269295518 Reorder the terms: 1 + B = -1.269295518 Solving 1 + B = -1.269295518 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + B = -1.269295518 + -1 Combine like terms: 1 + -1 = 0 0 + B = -1.269295518 + -1 B = -1.269295518 + -1 Combine like terms: -1.269295518 + -1 = -2.269295518 B = -2.269295518 Simplifying B = -2.269295518Solution
The solution to the problem is based on the solutions from the subproblems. B = {0.269295518, -2.269295518}
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